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A class of ${C^*}$-algebras generalizing both graph algebras and homeomorphism ${C^*}$-algebras III, ideal structures

Published online by Cambridge University Press:  14 November 2006

TAKESHI KATSURA
TAKESHI KATSURA
Affiliation:
Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, 060-0810, Japan (e-mail: katsura@math.sci.hokudai.ac.jp)
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Abstract

We investigate the ideal structures of the $C^*$-algebras arising from topological graphs. We give a complete description of ideals of such $C^*$-algebras that are invariant under the so-called gauge action, and give a condition on topological graphs so that all ideals are invariant under the gauge action. We get conditions for our $C^*$-algebras to be simple, prime or primitive. We completely determine the prime ideals, and show that most of them are primitive. Finally, we construct a discrete graph for which the associated $C^*$-algebra is prime but not primitive.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 6 , December 2006 , pp. 1805 - 1854
Copyright
2006 Cambridge University Press

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